Classification of Integrable One‐Component Systems on Associative Algebras

By Peter J. Olver, Jing Ping Wang. 2000

56 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/de53515364eb76009e6d269f7af98c8454a54ffa

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. V. Sokolov
2. A. Mikhailov
3. A. Alexandrou Himonas
4. Yue Liu
5. Changzheng Qu
6. Zhaoyang Yin
7. Katelyn Grayshan

In Geometry and Topology

1. V. Novikov
2. V. Sokolov
3. A. Mikhailov
4. A. Alexandrou Himonas
5. Yue Liu
6. Changzheng Qu
7. Zhaoyang Yin
8. Katelyn Grayshan

In Statistical and Nonlinear Physics

1. V. Novikov
2. V. Sokolov
3. A. Mikhailov
4. Zhaoyang Yin
5. Xing-Ping Wu
6. A. Alexandrou Himonas
7. Yue Liu
8. Changzheng Qu

Citations in the corpus

• Perturbative symmetry approach (2002, background): “The symbolic representation has been extended and proved to be very useful in the case of noncommutative differential rings [9].”
• Integrable systems and their recursion operators (2001, unknown): “A list of scalar equations with one symmetry was found in [OS98] and these equations were proved to be integrable in [ OW00 ].”
• Symmetries of Differential Equations and the Problem of Integrability (2009, result): “We introduce a weighting scheme by assigning a weight m = deg u to the dependent variable and n = deg x to the independent variable, so that the kth order derivative of u with respect to x has weight m + kn. Without loss of generality, we assume that n = 1. It was proved in [ 52 , 53] that for any i”